Development of a model for calculating the longwave optical properties and surface temperature of a curved venetian blind

This article is about the development of a mathematical model for calculating the longwave optical properties of a curved venetian blind. The calculated optical properties are used to determine the performance of the glass window installed with a venetian blind in terms of thermal comfort. The blind, whose optical properties are considered nonspecular, is modeled as an effective layer. The effect of slat curvature is included in the developed model. A six surface enclosure formed by two consecutive slats is used to analyze for the longwave optical properties of the effective layer. The longwave optical properties, transmittance, reflectance, absorptance and emittance are developed by using the radiosity method. The steady state energy balance method along with the developed longwave optical properties are used to determine the surface temperature of the effective layer. The empirical expression for the total heat flux from the indoor glass window surface with an adjacent venetian blind is adopted in the developed model. The surface temperature of the blind, which is the key parameter for calculating the thermal performance of glass windows with venetian blinds with respect to thermal comfort, is chosen as the parameter used for the model validation. The predicted surface temperature of the venetian blind is compared with the surface temperature of the venetian blind obtained from the measurement. The agreement between the predicted temperature and the measured temperature is good.     

Three-dimensional simulation with a CFD tool of the airflow phenomena in single floor double-skin facade equipped with a venetian blind

Nowadays different kinds of double-skin facades are developed and used in new architectural projects. The aim of these facades is, on the one hand, to increase internal comfort and, on the other hand, to decrease energy consumption. In order to optimise the overall performance of the double-skin façades, their detailed behaviour needs to be better understood. The prediction of the airflow within the channel (between the two glazings) is very important for understanding of the double-skin facades behaviour, especially in summer conditions. A comprehensive modelling of a compact double-skin facade equipped with a venetian blind and forced ventilation is proposed here. The modelling is done using the CFD (computational fluid dynamics) approach to assess the air movement within the ventilated facade channel. Three-dimensional airflow is modelled using a homogeneous porous media representation, in order to reduce the size of the mathematical model. A parametric study is proposed here, analysing the impact of three parameters on the airflow development: slat tilt angle, blind position and air outlet position. The distance between the blind and the external glazing was found to have a major impact on the velocity profiles inside the double-skin facade channel.     

Development of a mathematical model for predicting water vapor mass generated in micro-explosion

This paper describes a mathematical model for predicting the mass of water vapor generated in micro-explosion. First, a single droplet experiment was carried out. A W/O (water/oil) emulsified fuel droplet suspended by a thermocouple was heated by a halogen spot heater, and micro-explosion was observed using a high-speed video camera. The progress of the coalescence of the dispersed water droplet was observed while droplet was heated, and an aggregated water droplet was formed in the oil layer. Based on the measured micro-explosion characteristics, a mathematical model for predicting water vapor mass generated in micro-explosion was proposed. The size of the aggregated water droplet just before micro-explosion was measured to verify the proposed mathematical model. Under certain assumptions, mass and energy conservation equations were applied to micro-explosion process, and an equation to calculate water vapor mass generated in micro-explosion was derived. The derived equation and some measurement results provide enough information to calculate water vapor mass generated in micro-explosion. The calculated diameter of the water droplet, which changed to vapor in micro-explosion, was compared to that of the aggregated water droplet just before micro-explosion. The calculated results roughly agreed with experimental ones, and the validity of the proposed model was verified.     

A mathematical model of thermal performance of a solar air heater with slats

A mathematical model for computing the thermal performance of a single pass flat-plate solar air collector is presented. Air channels were formed by providing metal slats running along the circulated air passage linking the absorber plate by the bottom one in an endeavor to enhance the thermal efficiency of the solar air collector. A mathematical model, therefore, is developed by which the influence of the addition of the metal slats on the efficiency of the solar collector is studied. A computer code that employs an iterative solution procedure is constructed to solve for the governing energy equations to estimate the mean temperatures of the collector. The effect of volume airflow rate, collector length, and spacing between the absorber and bottom plates on the thermal performance of the present solar air heater was investigated. Furthermore, a numerical comparison of the present design with the most common type of solar air heaters is conducted. The results of the comparison have indicated that better thermal performance was obtained by the modified system.     

A mathematical model of variable displacement wobble plate compressor for automotive air conditioning system

Based on the force balance equations, mass and energy conservation equations, a mathematical model of control valve used in the variable displacement wobble plate compressor (VDC) is developed firstly. The dynamic model of the moving components is developed then by analyzing the forces and force moments acting on the piston, piston rod, wobble plate, rotating journal and shaft sleeve. The compression process model is obtained by fitting the data from our experiments. And finally the steady-state mathematical model of VDC is developed by combining the three models above. In order to verify the mathematical model of compressor, a test bench for the control valve and the test system for the VDC have been established, and the simulated results agree well with the experimental data. The simulation results show that there are four operation modes for the VDC, i.e. constant rotary speed and constant piston stroke length (PSL), variable rotary speed and constant PSL, constant rotary speed and variable PSL, variable rotary speed and variable PSL, which have included almost all operation modes of the refrigeration compressor in common use.     

Determination of nanolayer thickness for a nanofluid

Recent core–shell–medium models as a modification of the traditional effective medium theories for explaining the enhanced thermal conductivity of nanofluids are semi-empirical. Generally, the resulting thickness and conductivity of the nanolayer both have to be chosen to match the measured thermal conductivity of the nanofluid. Here, we attempt to find a more systematic procedure to determine the nanolayer thickness and the thermal conductivity profile within the nanolayer. An expression for the nanolayer thickness is derived by manipulation of the three basic heat conduction regions. Comparison of the estimated thermal conductance with known experimental data and thermal diffusion length are made.     

Application of mathematical model for the process of coal tar pitch modified petroleum asphalt

This paper firstly discusses the properties of modified asphalt by blending petroleum asphalt and coal tar pitch. Then, a new mathematical model which was called ZQL was constructed. Based on three variables, property, granularity size, and proportion, the three-dimension function was fit, where the property was set as a dependent variable and the rest of the variables were set as independent variables. The different functions were finally obtained. Finally, based on the British standard of road asphalt, we solve the ZQL model and obtain a suitable result which matches the experimental results very well.     

Application of a detailed mathematical model to the gasifier unit of the dual fluidized bed gasification plant

A one-dimensional steady state model for biomass-steam gasification has been developed. The reactor is a bubbling fluidized bed. With respect to hydrodynamics the model distinguishes two zones namely: dense zone and freeboard zone. The gasification process is modelled in three steps: drying, devolatilization and gasification of biomass char. The model assumes that solids are well mixed while the gases are in plug flow regime. Mass and energy balance is solved globally across the entire gasifier. The gas composition and temperatures predicted by the model for wood chips as fuel agree well with values measured at an 8 MW (fuel power) commercial plant.     

A mathematical model for the anodic half cell of a dye-sensitised solar cell

We present a mathematical model of the steady-state current produced by the anodic half cell of a dye-sensitised solar cell (DSC) under both illuminated and non-illuminated conditions. A one-dimensional transport model that describes the transport of charged species via migration and diffusion within the electrolyte filled pores and the porous semiconductor that constitutes the porous anode of the DSC is given. This model is coupled to an interfacial model, developed previously by the authors, that describes charge transfer across the semiconductor–dye–electrolyte interface by explicitly accounting for each reaction at the interface involving dye molecules, electrolyte species, and semiconductor electrons. An equivalent circuit extension to the anode model (in the form of a boundary condition) is developed in order to validate some of the simulation results of the anode model with experimental results obtained from a full DSC specifically commissioned for the study. Parameter values associated with the model are obtained from the literature or experimentally from the specifically commissioned cell. A comparison of the numerical simulation results with experimental results shows a favourable correspondence without the need to fit parameter values.     

Development of a mathematical model for optimizing a heliostat field layout using differential evolution method

In this study, differential evolution was employed to perform optimization of a heliostat field. A complete mathematical code was developed for this purpose, which generates a heliostat field and calculates the optimum spacing between heliostats through differential evolution optimization technique. The optimization was executed for two sets of two cases and compared with an un‐optimized case. In the first case, only the optical performance was optimized, whereas in the second case, the normalized ratio of the optical performance to the land area covered by the heliostat field was maximized. In the first set of cases, the extra security distance between the heliostats was neglected, whereas in the second set of cases, the extra security distance was taken into account. To apply and examine the application of the optimization algorithm developed, 3 days of the year were selected: March 21, June 21, and December 21, considering Dhahran, Saudi Arabia as an illustrative example. For June 21, when the extra security distance between the heliostats is neglected, the optical efficiency of the un‐optimized case was 0.6026, while for the first optimized case, it was 0.6395, and for the second optimized case, it was 0.6033. However, when the extra security distance was considered, the optical efficiency of the un‐optimized case was 0.6167; while for the first optimized case, it was 0.6241, and for the second optimized case, it was 0.6167. Similar observations were realized for the other cases selected. Copyright © 2015 John Wiley & Sons, Ltd.     

Assessment of an “Energy Tower” potential in Australia using a mathematical model and GIS

“Energy Tower” is a technology for producing renewable and clean electricity by means of cooling hot and dry air, which is continuously supplied to arid lands. We assess the potential of an Energy Tower by incorporating topographic and meteorological parameters into a computational model, providing evaluations for the net power production and the electricity production cost. We formulate a highly simplified model for the Energy Tower’s flow, setup and process a spatial dataset of topographic and Meteorological upper air parameters. The model was applied to the Australian continent. A model simulation of one annual cycle enabled the ranking and selection of promising sites. The highest potential for energy towers is in the Port Hedland region, where favorable meteorological and topographic conditions would result in high average net power (≈370 ± 160 MW), potentially providing the electricity needs of 0.5 million people, for an economically competitive costs (3.5 ¢kWh).     

A mathematical model for interfacial charge transfer at the semiconductor–dye–electrolyte interface of a dye-sensitised solar cell

A mathematical model for the interfacial charge transfer within dye-sensitised solar cells (DSC) is presented for the semiconductor–dye–electrolyte interface. The model explicitly accounts for each reaction at the interface involving dye molecules, electrolyte species and adsorbed electrons associated with the conduction band surface states of the semiconductor. Additionally, the model accounts for photoelectron injection via singlet and triplet excited dye states. The governing equations can be used to describe the total current produced by the DSC under illuminated and non-illuminated conditions, at steady state. Regular perturbation methods are applied to the model equations to obtain closed form analytic approximations, resulting in approximate solutions that negate the need for numerical solution of the model system. All parameter values associated with the model are obtained from the literature and from experimental data. The presented numerical results and analytic approximations compare favourably to experimental data, capturing the interfacial characteristics of current versus voltage curves of the DSC.     

Optimum insulation thickness of the piping system with combined economic and environmental method

In the present study, an alternative method combining economic and environmental costs is suggested for the pipe insulation. This method is called as combined economic and environment method (CEEM). Bilecik, which is located in the Marmara region, Turkey, is chosen. Rockwool and glass wool are chosen as insulation materials. The optimum insulation thicknesses of three different methods including CEEM, economic, and environmental approaches are calculated and compared. Optimum points are 0.46 m (CEEM), 0.39 m (economic approach), and 0.54 m (environmental approach) for rockwool; and 0.46 m (CEEM), 0.40 m (economic approach), and 0.59 m (environmental approach) for glass wool. In addition, annual cost savings and energy savings are determined.     

A dynamic mathematical model of a shell-and-tube evaporator. validation with pure and blend refrigerants

This work presents a mathematical model of a shell-and-tube evaporator based on mass continuity, energy conservation and heat transfer physical fundamentals. The model is formulated as a control volume combination that represents the different refrigerant states along the evaporator. Since the model is based on refrigerant and secondary fluid states prediction, it can be easily adapted for modelling any type of evaporator. The strategy of working with physical fundamentals allows the steady- and dynamic-state analysis of any of its performance variables. The paper presents a steady-state validation made with two pure refrigerants (HCFC-22, HFC-134a) and with a zeotropic blend (HFC-407C), and a dynamic validation with transient experimental tests using HCFC-22. The model prediction error is lower than 5% and it is well in accordance with actual dynamic behaviour. Copyright © 2006 John Wiley & Sons, Ltd.     

Development of a pyrolysis model for corrugated cardboard

The current study outlines a general approach to construct a one-dimensional pyrolysis model based on milligram-scale and bench-scale test data collected systematically to isolate a specific process in each test. This approach is demonstrated by developing a model of burning for corrugated cardboard. Thermogravimetric analysis and differential scanning calorimetry were conducted on pulverized cardboard to determine the thermal degradation mechanism, the enthalpy of decomposition reactions, and the heat capacities of apparent species. Data collected in pyrolysis-combustion flow calorimetry tests were analyzed to assign a heat of combustion to the volatiles evolved from each reaction. Bench-scale tests were conducted with a cone calorimeter on samples in a horizontal orientation to observe the flaming combustion of this material at external heat fluxes ranging from 20 to 80 kW m⁻². Condensed phase temperature data was collected in these tests to measure and infer thermal transport properties and to characterize property changes associated with thermal degradation through an iterative inverse analysis. All the parameters determined through analysis of the milligram-scale and bench-scale tests were used to construct a one-dimensional pyrolysis model that predicted the average mass loss and heat release rates from cone calorimeter tests to within, on average, 17% and the times to ignition to within 2 s.     

一种损失和落后角模型在轴流压气机特性预估中的应用

为了得到某型两级轴流压气机的特性曲线，采用在子午平面上叶片排间隙中设置计算站的流线曲率法对其内流场进行了数值模拟，得到子午平面上速度分布；建立了一种设计、非设计损失和落后角模型的组合，将其应用到两级压气机特性计算当中去，得到了不同转速条件下，压气机特性的变化曲线，将其同试验得到的特性线作对比，验证了损失和落后角模型在压气机特性计算当中的有效性。     

A mathematical model to analyze heat and mass transfer characteristics of a CPL evaporator porous wick

A capillary pumped loop (CPL), because of its high power thermal transport character, has been developed as an attractive system for the thermal discharge of electronic chips with high power loads, especially on spacecrafts. A working fluid having relatively larger heat of evaporation, methanol for example, may transfer significant heat flux. In this paper a new mathematic model is constructed, in which the most important character is the treatment or the unsaturated region of the evaporator porous wick. Numerical simulation of heat and mass transfer in the evaporator porous wick is carried out with a new three‐layer model. The importance of unsaturated layer to simulate the present problem is clear. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(4): 209–218, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20066     

A mathematical model of a tubular solid oxide fuel cell with specified combustion zone

A numerical model has been developed to simulate the effect of combustion zone geometry on the steady state and transient performance of a tubular solid oxide fuel cell (SOFC). The model consists of an electrochemical submodel and a thermal submodel. In the electrochemical model, a network circuit of a tubular SOFC was adopted to model the dynamics of Nernst potential, ohmic polarization, activation polarization, and concentration polarization. The thermal submodel simulated heat transfers by conduction, convention, and radiation between the cell and the air feed tube. The developed model was applied to simulate the performance of a tubular solid oxide fuel cell at various operating parameters, including distributions of circuits, temperature, and gas concentrations inside the fuel cell. The simulations predicted that increasing the length of the combustion zone would lead to an increase of the overall cell tube temperature and a shorter response time for transient performance. Enlarging the combustion zone, however, makes only a negligible contribution to electricity output properties, such as output voltage and power. These numerical results show that the developed model can reasonably simulate the performance properties of a tubular SOFC and is applicable to cell stack design.     

A simple model for explosive combustion of premixed natural gas with air in a bubbling fluidized bed of inert sand

The combustion of premixed natural gas and air has been studied in a bubbling fluidized bed of inert particles. The temperature of the solids was carefully monitored, using 8 thermocouples, immersed in the bed at different heights. The observed temperature profiles were used to find the height above the distributor at which most of the combustion occurred and on this basis a clear distinction could be made between combustion above the bed and inside the bed. The region where most of the heat of combustion is evolved depends on the average bed temperature. If this temperature is low, the gases burn above the bed or just under its upper surface, but at higher temperatures the process is located close to the distributor. Rapid fluctuations in the measured temperature and pressure indicate that the process inside the bed is not a steady one. The model developed here assumes that combustion takes place inside bubbles of premixed gases, as they move through the bed. A detailed chemical kinetic model was used to calculate the induction period for ignition. The model can predict the height above the distributor at which bubbles should ignite and explode. Comparison of the experimental results with the modeling calculations indicates that the course taken by the process depends on temperature. At the lowest temperatures, the gases burn above the bed. In the high temperature range, where the bubbles ignite is determined by the induction period. At intermediate temperatures the location of the reaction is determined by the depth of the bed and bubble size, with ignition spreading from above the bed to bubbles, which are about to leave, but are still in the bed. That bubbles explode at different heights up the bed is reflected in the acoustic signals registered above and below the bed. The associated changes in the composition of the flue gases are also very characteristic.